zbMATH — the first resource for mathematics

On the use of words and fuzzy sets. (English) Zbl 1098.03066
The intent of this study is to identify possible linkages between fuzzy sets and computing with words and perceptions by stressing that fuzzy sets are formal entities giving rise to the extension of predicates (gradable predicates, to be more specific). The paper starts with a concise discussion on sets and predicates and then concentrates on the on gradable (imprecise) predicates. Some observations are made with regard to antonyms in this setting and the role played by $$L$$-fuzzy sets. Finally, some projections are offered with respect to the roadmap of the development of fuzzy sets and computing with words.

MSC:
 03E72 Theory of fuzzy sets, etc. 68Q05 Models of computation (Turing machines, etc.) (MSC2010)
Full Text:
References:
 [1] deLuca, A.; Termini, S., A definition of a non-probabilistic entropy in the setting of fuzzy sets theory, Inform. control, 20, 4, 335-373, (1972) [2] Ganter, B.; Willie, R., Formal concept analysis, (1996), Springer [3] Goguen, J., The logic of inexact concepts, Synthese, 19, 335-373, (1968) · Zbl 0184.00903 [4] Halmos, P.R., Naïve set theory, (1960), Van Nostrand · Zbl 0117.10502 [5] Mamdani, E.H., A misconception of theory and application, IEEE expert, August, 40-41, (1994) · Zbl 1009.03525 [6] S.A. Orlovski, Calculus and properties of fuzzy sets, in: Proc. 4th. IFSA Conference (Brussels), 1991, pp. 153-157. [7] Russell, B., The principles of mathematics, (1973), Routledge London [8] M. Sugeno, Theory of fuzzy integrals and its application, Ph.D. dissertation, Tokyo Institute of Technology, 1974. [9] Terricabras, J.M.; Trillas, E., Some remarks on vague predicates, Theoria, 10, 1-12, (1988) [10] Trillas, E.; Alsina, C., A reflection on what is a membership function, Mathw. softcomput., 6, 201-215, (1999) · Zbl 0968.28013 [11] Türksen, I.B., Computing with descriptive and veristic words: knowledge representation and reasoning, (), 297-328 [12] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 33-50, (1965) · Zbl 0139.24606 [13] Zadeh, L.A., The concept of linguistic variable and its application to approximate reasoning, parts I, II, III, Inform. sci., 8, 199-249, (1975), 8 (1975) 301-357; 9 (1975) 43-80 · Zbl 0397.68071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.